Hi,
I'm new to Maxima and would like to calculate a full integration of
%e^(-(x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2-2*r*(x1*x2+x3*x4+x5*x6+x7*x8)-2*s*(x1*x3+x2*x4+x1*x5+x2*x6+x4*x8+x3*x7+x5*x7+x6*x8)-2*t*(x1*x4+x2*x3+x1*x6+x2*x5+x1*x7+x3*x5+x2*x8+x4*x6+x5*x8+x6*x7+x8*x3+x4*x7))/L).
Here the parameters L, r, s and t satisfy L>0, r^2+s^2+t^2+2*r*s*t<1,
r^2+s^2<1, r^2+t^2<1 and s^2+t^2<1. The first two
steps of the integration are just fine. However, I came across a problem
during carrying out the third integration step. It asks me if t^2+s^2-1 is
positive or negative! I couldn't figure out why it ask this stupid question.
Since
I know that the t^2+s^2-1 is negative, I just answer the question. But it
asks me another question about the positive or negative, because the
x1,x2,...,x8 are all variables and I could not define its sign. This
question almost
drives me mad.
Here's the execution results:
(%i1) assume(L>0,r^2<1,s^2<1,t^2<1,r^2+s^2+t^2+2*r*s*t<1,t^2+s^2<1,r^2+s^2<1,r^2+t^2<1);
integrate(%e^(-(x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2-2*r*(x1*x2+x3*x4+x5*x6+x7*x8)-2*s*(x1*x3+x2*x4+x1*x5+x2*x6+x4*x8+x3*x7+x5*x7+x6*x8)-2*t*(x1*x4+x2*x3+x1*x6+x2*x5+x1*x7+x3*x5+x2*x8+x4*x6+x5*x8+x6*x7+x8*x3+x4*x7))/L),x8,minf,inf);
(%o1) [L>0,r^2<1,s^2<1,t^2<1,-t^2-2*r*s*t-s^2-r^2+1>0,-t^2-s^2+1>0]
(%o2) blablabla...
(%i3) integrate(%o2,x1,minf,inf);
(%o3) blablabla...
(%i4) integrate(%o3,x3,minf,inf);
Is t^2+s^2-1 positive,negative, or zero? negative;
Is s(t(2x7+4x6+4x4)+2x7+2rx2)+... positive, negative, or zero? <= Here's the
problem!
Can anyone give me a help or some suggestions? Thanks!
--
Lin Xie
Beijing National Center for Electron Microscopy
Department of Material Science and Engineering
Tsinghua University
Beijing, PR of China